@article{3044559,
    title = "ALGEBRAIC IDEALS OF SEMIPRIME BANACH-ALGEBRAS",
    author = "GIOTOPOULOS, S and ROUMELIOTIS, M",
    journal = "Glasgow Mathematical Journal",
    year = "1991",
    volume = "33",
    number = "3",
    pages = "359-363",
    publisher = "Oxford Univ Press, Oxford, United Kingdom",
    issn = "0017-0895, 1469-509X",
    doi = "10.1017/S0017089500008429",
    abstract = "If A is a semiprime Banach algebra, soc A, rad A the socle and radical
of A, then soc A intersect rad A = (0).  This elementary result enables
us to prove some results concerning algebraic ideal and algebraic
elements modulo the socle of A.  We also deduce several conditions for A
equivalent to the condition dim A < + infinity."
}